A body slides down a frictionless track which ends in a circular loop of diameter $D$, then the minimum height $h$ of the body in term of $D$ so that it may just complete the loop, is
$h = \frac{{5D}}{2}$
$h = \frac{{5D}}{4}$
$h = \frac{{3D}}{4}$
$h = \frac{D}{4}$
A particle is projected from a horizontal plane such that its velocity vector at time $t$ is given by $\vec v = a\hat i + (b - ct)\hat j$ . Its range on the horizontal plane is given by
Two cars of masses $m_1$ & $m_2$ are moving along the circular paths of radius $r_1$ & $r_2$ respectively. Their speeds are such that they complete one round in same time. The ratio of angular speeds of two cars is
A point $P$ moves in counter clock wise direction on a circular path as shown in figure. The movement of $'P'$ is such that it sweeps out a length $S = t^3 + 5$, where $'S'$ is in meter and $t$ is in seconds. The radius of the path is $20\, m$. The acceleration of $'P'$ when $t = 2\, sec$. is nearly ......... $m/s^2$
Two seconds after projection a projectile is travelling in a direction inclined at $30^o$ to horizontal, after one more second it is travelling horizontally. What is the magnitude and direction of its velocity at initial point